Elasto-Plastic Analysis of Steel Beams

Abstract

In the modern structural design the limit state analysis of steel structure is obligatory. It is assumed that structure behave elastic until the maximum stress reaches the yield stress in the critical section. As the bending moment is increased, yielding spreads towards the neutral axis until the section has become the plastic hinge. At that stage the bendig moment is equal to plastic moment of the section. The limit state design is based on plastic hinge theory. This analysis includes calculation of internal forces by linear theory using specific load factors to produce structure against collaps.This approach is idealisation of the true section behaviour. In fact, the bending moments at sections adjacent to the critical one are sufficient to cause yielding before the plastic hinge can be formed. The result is gradual spreading of plasticity, both by depth of cross section and along the beam element. This causes a gradual bending of beam rather than sharp kink which would result from an idealised plastic hinge. In this paper effect of spreading of yield through the beam axis and over the depth of the beam is carryed out by finite element method (FEM). The continuous beam is analysed using the elasto-plastic Timoshenko beam theory and layer approach. The influence of the cross section stiffness, number of finite elements, number of layers as well as strain hardening parameter on the development of the plastic zone and on the ultimate limit state are presented.